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In order to achieve high-performance fault diagnosis of analog circuit, an analog circuit fault diagnosis method based on Wavelet Packet Energy Entropy(WPEE) and Random Forest(RF) is proposed. Select the appropriate test excitation signal, perform five-layer wavelet packet decomposition on the monitoring data, calculate the multi-band WPEE vector to characterize the fault features, and implement the fault diagnosis by RF classifier. The experimental results show that this method has good performance in the tolerance fault diagnosis of the biquadratic filter circuit, the Sallen-key filter circuit and the integrated fault diagnosis of the logarithmic amplifier circuit. The fault diagnosis accuracy in the experiment is more than 99%. This method has good parameter robustness, and the RF model has short training time. Compare with the method based on support vector machine and BP network, it shows better comprehensive performance and is more applicable to practice applications.